The Senate bill would end the shutdown, fund the government through Jan. 15 and raise the debt ceiling until Feb. 7. It also calls for a budget conference between the House and Senate that would have to report back by Dec. 15, and requires stricter income verification for recipients of ObamaCare subsidies.

Rep. Devin Nunes (R-Calif.) told The Hill that the Senate is likely to vote on the bill around 5 p.m. and then the House would vote closer to 9 p.m. He also said the House would leave town after the vote and return on Tuesday.

Lawmakers are trying to get a bill to President Obama's desk before the U.S. Treasury reaches its borrowing limit on Thursday.

The stock market was volatile throughout the more than two-week government shutdown and several financial institutions threatened to downgrade the U.S. credit rating if the U.S. defaulted on its debt.